Geodesic
Differential inclusions with unbounded right-hand side. Existence and relaxation theorems
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 3, pp. 246-262

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A differential inclusion in which the values of the right-hand side are nonconvex closed possibly unbounded sets is considered in a finite-dimensional space. Existence theorems for solutions and a relaxation theorem are proved. Relaxation theorems for a differential inclusion with bounded right-hand side, as a rule, are proved under the Lipschitz condition. In our paper, in the proof of the relaxation theorem for the differential inclusion, we use the notion of $\rho-H$ Lipschitzness instead of the Lipschitzness of a multivalued mapping.
Keywords: unbounded differential inclusions, existence and relaxation theorems. 
@article{TIMM_2014_20_3_a16,
     author = {A. A. Tolstonogov},
     title = {Differential inclusions with unbounded right-hand side. {Existence} and relaxation theorems},
     journal = {Trudy Instituta matematiki i mehaniki},
     pages = {246--262},
     publisher = {mathdoc},
     volume = {20},
     number = {3},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TIMM_2014_20_3_a16/}
}
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A. A. Tolstonogov. Differential inclusions with unbounded right-hand side. Existence and relaxation theorems. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 20 (2014) no. 3, pp. 246-262. http://geodesic.mathdoc.fr/item/TIMM_2014_20_3_a16/